Why Factorials? Treatment vs Design Structure
One Factor at a Time
What are we missing?
Incidence of high blood pressure in the United States continues to rise, and optimal strategies for treatment remain an open question. Most physicians agree that effective treatment likely involves a combination of lifestyle changes and medication, rather than relying on a single approach.
Researchers plan to study middle-aged U.S. women with moderate hypertension who are otherwise healthy (i.e., eating a standard diet and not taking regular medications).
Goal: Identify optimal combinations of diet and medication for lowering and maintaining blood pressure as measured by the change in blood pressure (mmHg) for each participant.
Diet (2 levels):
Medication (4 levels):
200 volunteers who meet the study inclusion criteria are recruited.
Researchers then find:
Is the optimal strategy to recommend the Mediterranean diet and ACE inhibitors together?
Each participant is randomly assigned to one combination of:
This results in t = _____ treatment combinations, with r = _____ participants per combination.
What can we learn from Design B that we can’t from Design A?
Definition: Full Factorial \((a \times b\times c \times ...)\)
A full factorial treatment structure (e.g., 2x2x2, 3x2 or 2x2, etc.) is a study in which there are two or more factors. Each factor will have at least two levels. The factor levels are combined to create the treatments (or treatment combinations).
Example: 2 diets x 4 medications
Example (Extended): 2 diets x 4 medications x 2 exercise routines
Diet and Medication treatment combinations are assigned to middle-aged U.S. women with moderate hypertension who are otherwise healthy (e.u.) in a CRD with r = 25. The change in blood pressure (mmHg) is measured for each woman in the study (m.u.).
library(edibble)
library(tidyverse)
des <- design(name = "BP 2 x 4 Full Facotrial CRD") |>
set_units(woman = 200) |>
set_trts(Diet = c("Standard American",
"Mediterranean"),
Medication = c("Diuretic",
"ACE",
"Beta blocker",
"Placebo")
) |>
allot_trts(Diet*Medication ~ woman) |>
assign_trts("random")
factorial_table <- serve_table(des)
factorial_table$change_bp <- NA
head(factorial_table)# An edibble: 6 x 4
woman Diet Medication change_bp
<U(200)> <T(2)> <T(4)>
<chr> <chr> <chr> <lgl>
1 woman001 Standard American Beta blocker NA
2 woman002 Mediterranean ACE NA
3 woman003 Standard American Beta blocker NA
4 woman004 Mediterranean Beta blocker NA
5 woman005 Standard American Placebo NA
6 woman006 Mediterranean Diuretic NA
DOE > Classical > Full Factorial